Record players have made a comeback over the past decade. Some of the credit probably goes to the hipster trend toward retro everything, but music lovers often claim records just sound better than digital music. I played my part in boosting record player sales after finding my mom’s old record collection in my parents’ house. The collection itself was not particularly exciting, but the possibility of listening to the exact records she had played as a teenager felt like some sort of time travel.

So we bought a record player. I distinctly remember playing The Beatles’ Sgt. Pepper’s Lonely Hearts Club Band. I had dutifully met the college student stereotype of blasting The Beatles on a regular basis, so I had heard those songs a hundred times. But when the cacophony at the end of “A Day in the Life” came on, it was not the one I had heard before. It sounded much deeper and fuller, like there were new noises in it. I was skeptical of the claim that vinyl sounded better, so I was surprised to be hearing a difference. Being a scientific-minded person, I’m not exactly swayed by one data point, but the experience did pique my curiosity.

So what’s the deal with the vinyl phenomenon? Is it really possible that records just inherently make a fuller sound? To have any hope of answering these questions, we have to start with something more basic: What is sound and how do we hear it?

All sounds are just vibrations in the air. You have likely seen sound visualized as a graph with many peaks and valleys. This graph is called a sound wave, and it shows how compressed the air is at a given point over time. Air disturbed by some noise source is funneled through the ear canal to a thin membrane called the eardrum. The vibrating air causes the eardrum to bounce back and forth in the same pattern as the disturbances in the air, and this pattern is sent to the brain to be interpreted as sound.

The human ear inspired the first audio recording device, invented in 1857 by Édouard-Léon Scott de Martinville. The machine was called a phonautograph. A horn played the role of the ear canal, taking air down to a thin piece of parchment. Like the eardrum, the parchment oscillated when vibrating air passed by it. But in the phonautograph the movement was transferred from the parchment to an attached stylus. A piece of paper then recorded the drawings made by the stylus. Each step of this process is a physical transfer of vibrations from one medium to another, so the end result is a curve showing the changes in air pressure that created the original sound. The fact that the drawings could contain enough information to reproduce the recorded sound did not appear to occur to de Martinville or his colleagues, but it’s hard to fault them for not immediately assuming a squiggle on a page could be used to reproduce complex sounds.

Analog playback came around in the 1870s, when French inventor Charles Cros had the ingenious idea to transfer the phonautograph recordings to a groove on a disc. If you zoom in on a single groove of a vinyl record and look at it from the side, the shape would resemble one of the phonautograph drawings. To play back the sound, the phonautograph’s process is reversed. A thin point, such as a needle, rides along the groove, moving up and down with the peaks and valleys encoded in the record. The needle is held by an arm, and the needle’s movement re-creates the same motion the stylus made during the original recording. This arm is then attached to a thin piece of some flexible material, which vibrates back and forth as dictated by the arm’s motion. The movement of the material disturbs the air, and the disturbances are amplified as they flow out of a horn. The vibrations in the air created by this play back method are the same as those that produced the original recordings. Because our ear interprets sound based entirely on the patterns of compression in the air, we hear the exact same sound that had been recorded.

The mechanics of this process seem reasonable enough. Sound is defined by vibrations in the air. Disturbed air makes the phonautograph move in a particular way. Re-creating that motion makes still air vibrate the way it had before, so the same sound is reproduced. But tucked into this process is the entirely unintuitive claim that everything from David Bowie to Nina Simone to nails on a chalkboard can each be reduced to a single squiggle on a recorded groove.

If we want to figure this out, we need to know how the brain decides what listening experience to produce. Two key decisions the brain makes are what volume and pitch you will hear. Volume depends on the size of the peaks and valleys of a sound wave (which is called amplitude) and pitch is determined by how many peaks pass by your ear over the course of a second (which is called frequency). The larger the amplitude, the louder the noise; the higher the frequency, the higher the pitch. A band playing their hit song won’t produce sound waves that are uniform enough to easily pick out amplitude or frequency, but that’s okay. Sound waves with uniform amplitude and frequency are called pure tones, and these readily translate to some pitch and volume.

Of course, if a piano and a violin play the same high C at the exact same volume, there is still some quality that feels different between the two notes. It turns out that pure tones do not occur naturally, and when a piano or violin produces a high C, the sound wave is made up of a specific combination of different pure tones. The different amplitudes and frequencies have nice relationships with one another, which is why you hear a specific note rather than a mess of clashing noises, but the single pitch you hear does not correspond to a single frequency. The hard-to-define quality of sound that allows you to identify what instrument you’re listening to is determined by the exact combination of pure tones. When different instruments all play at the same time, the various pure tones add together to create the music you hear.

So what do pure tones have to do with the groove on a record being able to tell David Bowie and Nina Simone apart? It turns out that any curve can be written in exactly one way as a combination of curves with uniform amplitude and frequency. In other words, the single squiggle captured in the groove of a record player can be written as a combination of pure tones. And there is only one combination that will produce any particular squiggle. The tool that makes this possible comes from mathematics and is called the Fourier transform. Combined with the fact that the sound we experience is determined by the exact combination of pure tones, this bit of mathematics explains how the vinyl record groove can completely determine the music you hear.

When it comes to storing sound as a digital file, however, the limited capacity of computers is a problem. Sound waves contain an infinite number of points. Computers cannot store infinite amounts of information. Digital music storage is possible, thanks to the work of mathematicians in the 1930s that produced the sampling theorem. According to the theorem, it is possible to completely rebuild a sound wave using a finite number of points—as long as they are close enough together.

There is one catch: The theorem requires that when the Fourier transform breaks down the curve into a combination of pure tones, all the frequencies fall between some maximum and minimum. How close together the points on a curve need to be in order to rebuild it depends on the distance between this maximum and minimum. Because humans only hear sounds within a certain range of frequencies, we can get rid of any other frequencies that may show up in a sound wave’s decomposition and still get back the original sound. So the sampling theorem explains how to use a finite amount of information to store any sound wave.

Because mathematics describes an idealized version of reality, the reconstruction of a sound wave from a digital file may not perfectly match the vibrations of the sound itself. On the other hand, analog recording is purely physical. Does this mean analog is more accurate? No, it just means it’s different. Movement, dust or scratches can change the sound an analog player makes, and the recording process is similarly sensitive. The sound wave produced by analog playback could be further from the original than a good quality digital file would be.

Sound quality depends on a lot of factors, and it is impossible to definitively state that either analog or digital is fundamentally better. These days, many records are made using playback of a digital file, so vinyl preference cannot be attributed solely to the differences in the way the sound wave is reproduced. But the fact remains that analog captures a physical process whereas digital uses mathematics to reduce the process to finite bits of information. What, if anything, is lost in that reduction is difficult to pinpoint. But the limitations of math in replicating reality may factor in to the difference in listening experiences reported by so many vinyl lovers.

The views expressed are those of the author(s) and are not necessarily those of Scientific American.

ABOUT THE AUTHOR(S)

Katrina Morgan

Katrina Morgan is a Ph.D. candidate in pure mathematics at the University of North Carolina at Chapel Hill studying partial differential equations. She is also co-founder of the program Girls Talk Math, a free summer day camp for high schoolers identifying as girls who are interested in math.

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